“I don’t believe in a God who would distance Himself from such a man just for observing what I feel is common courtesy.”
Please do not take this the wrong way, but I cannot help but sense some confusion on your part about some aspects of being Torah observant. Hashem does not need our observance, stringencies, or good deeds – all mitzvot are there solely for our benefit entirely. In order for us to achieve closeness to Hashem, we must strive to be as pure as possible. Hashem is absolutely holy, and we can only aspire to some form of holiness as best we can by putting distance between ourselves and anything which is not holy in order to hope to establish some closeness to Hashem.
For many men this means to avoid interaction with women other than their immediate families and those women they must communicate with for work. Not because the women are not holy, but because the men find themselves having inappropriate thoughts. Yes it may seem like “all or nothing” but sometimes the best path to consistent observance is to make blanket exclusions in order to avoid what may really be the rare and passing failure to maintain a holy mind.
If you take this as rudeness, I feel you are making it too much about yourself and not about Torah, Hashem and kedusha. If you want to wish everyone you meet Gut Shabbos, go ahead, but if all your greetings are not returned, I respectfully suggest that you not focus on that and detract from the joy of that Shabbat, but go on your way, and keep a kind thought in your mind for the man you passed and know that his intention is certainly not to be rude to anyone, but to be as close to Hashem as he can.